Balanced random interval arithmetic in market model estimation

The possibility of estimating bounds for the econometric likelihood function using balanced random interval arithmetic is experimentally investigated. The experiments on the likelihood function with data from housing starts have proved the assumption that distributions of centres and radii of evaluated balanced random intervals are normal. Balanced random interval arithmetic can therefore be used to estimate bounds for this function and global optimization algorithms based on this arithmetic are applicable to optimize it. The interval branch and bound algorithms with bounds calculated using standard and balanced random interval arithmetic were used to optimize the likelihood function. Results of the experiments show that when reliability is essential the algorithm with standard interval arithmetic should be used, but when speed of optimization is more important, the algorithm with balanced random interval arithmetic should be used which in this case finishes faster and provides good, although not always optimal, values.